Universität Wien

250105 VO Ergodic Theory (2020W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

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Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Thursday 01.10. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 06.10. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 08.10. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 13.10. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 15.10. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 20.10. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 22.10. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 27.10. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 29.10. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 03.11. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 05.11. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 10.11. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 12.11. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 17.11. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 19.11. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 24.11. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 26.11. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 01.12. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 03.12. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 10.12. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 15.12. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 17.12. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 07.01. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 12.01. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 14.01. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 19.01. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 21.01. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 26.01. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Thursday 28.01. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß

Information

Aims, contents and method of the course

This is an introduction to ergodic theory, that is: the study of how invariant measures play a role in dynamical systems. Topics to be discussed are likely to include
- Invariant measures in various standard examples (both finite and infinite);
- Ergodicity, unique ergodicity and proving ergodicity;
- Poincaré recurrence and Kac' Lemma;
- Ergodic Theorems;
- Induced transformations, Rokhlin towers and similar results;
- Transfer operators;
- Connections to notions from Probability Theory (Mixing, Bernoulli processes).
The course will be given in English

Assessment and permitted materials

Oral examination (English but also possible in German)

Minimum requirements and assessment criteria

A fair understanding during the exam of the material covered during the course, specifically theorems, proofs or proof sketches, main examples and counter-example (to theorems if assumptions are missing)

Examination topics

The material covered in class (or if agreed a subset of this)

Reading list

There will be online classnotes. Background reading:
Peter Walters, An Introduction to Ergodic Theory, Springer-Verlag 1975 ISBN 0-387-95152-0.
Ricardo Mañé, Ergodic theory and differentiable dynamics, Ergebnisse der Mathematik und ihrer Grenzgebiete 8. Springer-Verlag, Berlin, 1987. ISBN: 3-540-15278-4
Daniel Rudolph, Fundamentals of measurable dynamics, Oxford Science Publications, Clarendon Press Oxford 1990 ISBN 0-19-853572-4
Karl Petersen, Ergodic Theory, Cambridge Studies in Advanced Mathematics, 1983, Cambridge University Press ISBN 0-521-38997-6
Michael Brin and Garrett Stuck, Introduction to Dynamical Systems, Cambridge University Press 2002, ISBN 0-521-80841-3
Omri Sarig, Lecture Notes on Ergodic Theory Penn State, Fall 2008,

Association in the course directory

MSTV

Last modified: Tu 13.12.2022 00:24